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QuestionA firm needs to deposit now to pay R6,285 per coffee machine in 4 months with 8%8\% annual simple interest. How much?

Studdy Solution

STEP 1

Assumptions1. The firm has ordered three coffee machines. The cost per machine is R6285,003. The machines will be delivered in four months4. The firm needs to keep an amount in a savings account to pay for the machines5. The savings account pays8% simple interest per year6. The interest is calculated as a one-time payment, not monthly compounding7. The firm wants to have exactly the amount needed to pay for the machines in the account when they are delivered

STEP 2

First, we need to find the total cost of the machines. We can do this by multiplying the cost per machine by the number of machines.
Total cost=Cost per machinetimesNumber of machinesTotal\, cost = Cost\, per\, machine \\times Number\, of\, machines

STEP 3

Now, plug in the given values for the cost per machine and number of machines to calculate the total cost.
Total cost=R6,285.00times3Total\, cost = R6,285.00 \\times3

STEP 4

Calculate the total cost of the machines.
Total cost=R6,285.00times3=R18,855.00Total\, cost = R6,285.00 \\times3 = R18,855.00

STEP 5

We know that the total cost is the amount in the account after four months of interest. Let's denote the amount that must be deposited now as. The relationship between these quantities can be expressed asTotal cost=times(1+Interest ratetimesTime)Total\, cost = \\times (1 + Interest\, rate \\times Time)

STEP 6

We need to solve this equation for. First, let's plug in the values for the total cost, interest rate, and time.
R18,855.00=times(1+8%times412)R18,855.00 = \\times (1 +8\% \\times \frac{4}{12})

STEP 7

Convert the percentage to a decimal value.
%=0.08\% =0.08R18,855.00=times(1+0.08times412)R18,855.00 = \\times (1 +0.08 \\times \frac{4}{12})

STEP 8

implify the equation.
R18,855.00=times(1+0.08times13)R18,855.00 = \\times (1 +0.08 \\times \frac{1}{3})R18,855.00=times(1+0.0266667)R18,855.00 = \\times (1 +0.0266667)

STEP 9

olve the equation for.
=R18,855.00+.0266667 = \frac{R18,855.00}{ +.0266667}

STEP 10

Calculate the amount that must be deposited into the savings account now.
=R18,855.00+0.0266667=R18,366.28 = \frac{R18,855.00}{ +0.0266667} = R18,366.28The firm needs to deposit R18,366.28 into the savings account now.

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